How do I gently bend 4 bottle sides inward simultaneously to create a uniform dent?
May I suggest a Lattice?



Create a Lattice object, and link it to the bottle with a Lattice modifier on the bottle object. Set the Lattice object to an acceptable resolution, and in Edit mode, move some lattice vertices closer to the center with the Scale transform tool. The deformation depends on the subdivision of the lattice and the selection of vertices. Experiment until you find the correct values for your situation.